§ Leverage and the Equity Cost of Capital
§ MM I states that
E + D = U = A
Where E and D are the market value of equity and debt, U is the
market value of equity is the firm is unlevered, and A the market
value of the firm’s assets
§ That is, the total MV of the firm’s securities is equal to the MV of its
assets, whether the firm is levered or unlevered
§ Leverage and the Equity Cost of Capital
§ The relation between returns of levered equity (R
E
), debt (R
D
), and
unlevered equity (R
U
) is:
EDU
ED
RRR
ED ED
+=
++
!
Risk without
leverage
Additional risk
due to leverage
( )
EU UD
D
RR RR
E
=+-
"##$##%
§ Leverage and the Equity Cost of Capital
§ This relation holds for realized returns and also expected
returns
§ MM II: The cost of capital of levered equity increases with the
firm’s market value debt-equity ratio
§ Cost of Capital of Levered Equity:
( )
EU UD
D
rr rr
E
=+ -
§ Capital Budgeting and the Weighted Average Cost of
Capital
§ MM propositions help us understand the effect of leverage on
the firm’s CoC for new investments
§ If a firm is financed with both equity and debt, the risk of its
underlying assets will match the risk of a portfolio of its equity
and debt
§ Capital Budgeting and the Weighted Average Cost of
Capital
§ In a world with no taxes, the firm’s WACC and unlevered cost
of capital coincide
§ With perfect capital markets, a firm’s WACC is independent of
its capital structure and is equal to its unlevered equity cost of
capital, which matches the cost o capital of its assets
wacc U A
rrr==
§ Capital Budgeting and the Weighted Average Cost of
Capital
§ Debt-to-value ratio is measured by D/(E+D)
§ With no debt, the WACC is equal to the unlevered equity cost
of capital
§ Even though debt and equity costs of capital both rise when
leverage is high, more weight on the lower-cost debt makes
WACC constant
§ Computing the WACC with Multiple Securities
§ r
u
and r
wacc
are calculated by computing the weighted average cost
of capital of all of the firm’s securities
